Final answer:
Union military victories in the fall of 1864, especially the fall of Atlanta and successes in the Shenandoah Valley, were the most direct factors that boosted Abraham Lincoln's popularity, leading to his reelection.
Step-by-step explanation:
The most direct factor affecting Abraham Lincoln’s reelection in 1864 was a series of Union victories that occurred in the fall of that year. Although facing strong anti-Lincoln sentiment and criticism for his wartime policies, such as the suspension of the writ of habeas corpus, Lincoln's prospects were bolstered significantly by military successes. The capture of Atlanta in September and General Philip Sheridan's triumphs in the Shenandoah Valley played a key role in shifting public opinion in Lincoln's favor. As a result of these Union victories, Lincoln won reelection by a wide margin in the Electoral College and received a strong show of support from Union army troops despite securing only 40 percent of the popular vote.